The era of Global Navigation Satellite System (GNSS) triple-frequency signals is approaching. Not only is this due to the modernization of United States (U.S.) Global Positioning System (GPS) and Russian GLObal NAvigation Satellite System (GLONASS), but also due to the emergence of other GNSS constellations including Galileo and BeiDou. Even with different frequency plans, each of the four GNSS systems may provide signals at more than three frequencies: L1/L2/L5 from GPS, L1-CDMA/L2-CDMA/L3-CDMA/L5-CDMA from GLONASS, E1/E5a/E5b/E6 from Galileo, and B1/B2/B3 from BeiDou.
Triple-frequency signals for different GNSS systems are generalized as GNSS-L1, GNSS-L2 and GNSS-L5, as listed in FIG. 1. As depicted, GPS L1, Galileo E1, BeiDou B1 and GLONASS L1-CDMA are represented as GNSS-L1. Similarly, GPS L2, Galileo E5b, BeiDou B3 and GLONASS L2-CDMA are represented as GNSS-L2. Additionally, GPS L5, Galileo E5a, BeiDou B2 and GLONASS L5-CDMA are represented as GNSS-L5. Three types of wide-lane (WL) combinations can be formed as shown in FIG. 2, with the maximum wavelength of 4.57-9.77 m using GNSS-L2 and GNSS-L5, and the minimum wavelength of 0.75-0.85 m using GNSS-L1 and GNSS-L5.
GNSS systems typically include three major components: earth-orbit satellites, ground control and tracking stations, and GNSS receivers. GNSS receivers have been used in various applications, including automobile navigation, emergency and location based services, tracking systems (e.g., for vehicles, persons, pets, or freight), marine navigations (e.g., for boats and ships), aircraft autopilot systems, real-time mapping, machine guidance at construction sites, mining, precision agriculture, land surveying, and deformation monitoring. Depending on the application, positioning accuracy requirements for the GNSS receivers may differ. For example, meter level accuracy is desirable for consumer grade receivers used for recreational and navigational purposes, while sub-meter level accuracy is desirable for mapping grade receivers for Geographical Information System (GIS) feature collection. Centimeter level accuracy is desirable for survey grade receivers. Currently there are two major GNSS precise positioning techniques used to achieve centimeter level accuracy: Real-Time Kinematic (RTK) and Precise Point Positioning (PPP).
As an alternative GNSS precise positioning technique to RTK, PPP is defined as the state-space solution to process pseudo-range and carrier-phase measurements from a single GNSS receiver by utilizing satellite constellation precise orbits and clock offsets determined by separate means. There are three key factors for PPP: precise orbit and clock, precise error source modeling, and the use of carrier phase measurements. PPP differs from RTK from several perspectives. Firstly, PPP eliminates the spatial operation limit because it has no regional base station requirement. The determination of precise GNSS orbit and clock to support PPP requires a global reference network, but its baseline length is normally hundreds to thousands of kilometers, which differs from RTK. Secondly, error source modeling of PPP is typically more complex than RTK. RTK uses the regional base station information to generate a double-difference, in which a majority of the error sources may be eliminated. Because local base stations are typically not available, the error sources affecting GNSS navigation accuracy in PPP have to be considered, such as atmospheric effects, relativistic effects, site displacements, antenna phase center corrections, and phase wind-up effects. Thirdly, PPP is a global positioning approach because its determined position solutions are referred to a global reference frame, and the corrections to support PPP (e.g., precise orbit and clock) are globally valid. However RTK provides local position solutions relative to the local base stations especially when the base coordinates are not precisely determined. Therefore PPP may provide better long-term repeatability and consistency than RTK. PPP has several advantages over RTK, but PPP requires a long time to converge the float ambiguity in order to ensure the centimeter level positioning accuracy, so this largely limits its adoption to real-time.
In Wang and Rothacher (2013), an ambiguity resolution method for triple-frequency geometry-free with an ionosphere-free combination for long baseline RTK was tested with real data. The data was not applicable to PPP because there was no consideration of the fractional biases for PPP ambiguities. Therefore, the triple-frequency GF IF linear combination methods discussed by Wang and Rothacher are insufficient for resolving PPP ambiguity in real world conditions.
In Li et al. (2013), consideration of PPP ambiguity resolution with GNSS triple-frequency measurement was discussed. After fixing the L2/L5 Extra Wide-Lane (EWL) and L1/L2 WL ambiguities, the new formed ionosphere-free measurement with L2/L5 WL and L1/L2 WL carriers was applied to improve the dual-frequency NL ambiguity resolution. However, Li's final PPP fixed solution still fully relies on the dual-frequency carrier phase and NL ambiguity resolution with ˜10 cm wavelength, which is not achievable reliably within a short period of time and is not satisfactory for industry grade GNSS product development. Therefore, Li does not show how to resolve PPP ambiguity using triple-frequency methods.
In Geng and Bock (2013), the PPP ambiguity resolution approach for GPS triple-frequencies was investigated independently, but based on their result the ambiguity fixing also needed several minutes, which failed to compete with RTK. For example, Geng summarizes that when multipath effects become stronger, the performance of triple-frequency PPP ambiguity resolution is deteriorated considerably, and the correct ambiguity resolution is at 78% of all epochs. The consideration of the ambiguity fractional bias (i.e., UPD) follows the conventional approach, in which the fractional bias is modeled as one value for each satellite. The conventional approach does not handle high measurement noise issues at triple-frequency ionosphere-free carrier phases. Therefore, the methods discussed by Geng and Bock are also insufficient for resolving PPP ambiguity in real world conditions.
In Shen and Gao (2002), a smoothing technique was applied to improve the PPP float solution performance. However Shen and Gao apply a smoothing technique only for the code measurement. Accordingly, the prior art still fails to provide a robust triple-carrier ambiguity resolution method for PPP that is capable of rapid ambiguity resolution in a variety of noise conditions.